iucr

commissions

principles
aperiodic crystals
biological macromolecules
quantum crystallography
crystal growth and characterization of materials
crystallographic computing
crystallographic nomenclature
crystallographic teaching
crystallography in art and cultural heritage
crystallography of materials
electron crystallography
high pressure
inorganic and mineral structures
international tables
journals
magnetic structures
mathematical and theoretical crystallography
neutron scattering
nmr crystallography
powder diffraction
small-angle scattering
structural chemistry
synchrotron and xfel radiation
xafs

congress

2020 iucr xxv
2017 iucr xxiv
2014 iucr xxiii
2011 iucr xxii
2008 iucr xxi
2005 iucr xx
2002 iucr xix
1999 iucr xviii
1996 iucr xvii
1993 iucr xvi
1990 iucr xv
1987 iucr xiv
1984 iucr xiii
1981 iucr xii
1978 iucr xi
1975 iucr x
1972 iucr ix
1969 iucr viii
1966 iucr vii
1963 iucr vi
1960 iucr v
1957 iucr iv
1954 iucr iii
1951 iucr ii
1948 iucr i

people

nobel prize

all
agre
anfinsen
barkla
boyer
w.h.bragg
w.l.bragg
brockhouse
de broglie
charpak
crick
curl
davisson
debye
deisenhofer
geim
de gennes
hauptman
hodgkin
huber
karle
karplus
kendrew
klug
kobilka
kornberg
kroto
laue
lefkowitz
levitt
lipscomb
mackinnon
michel
novoselov
pauling
perutz
ramakrishnan
roentgen
shechtman
shull
skou
smalley
steitz
sumner
thomson
walker
warshel
watson
wilkins
yonath

resources

commissions

aperiodic crystals
biological macromolecules
quantum crystallography
crystal growth and characterization of materials
crystallographic computing
crystallographic nomenclature
crystallographic teaching
crystallography in art and cultural heritage
crystallography of materials
electron crystallography
high pressure
inorganic and mineral structures
international tables
journals
magnetic structures
mathematical and theoretical crystallography
neutron scattering
NMR crystallography
powder diffraction
small-angle scattering
structural chemistry
synchrotron radiation
xafs

outreach

openlabs

calendar
OpenLab Costa Rica
IUCr-IUPAP-ICTP OpenLab Senegal
Bruker OpenLab Cameroon
Rigaku OpenLab Bolivia
Bruker OpenLab Albania
Bruker OpenLab Uruguay 2
Rigaku OpenLab Cambodia 2
Bruker OpenLab Vietnam 2
Bruker OpenLab Senegal
PANalytical OpenLab Mexico 2
CCDC OpenLab Kenya
Bruker OpenLab Tunisia
Bruker OpenLab Algeria
PANalytical OpenLab Turkey
Bruker OpenLab Vietnam
Agilent OpenLab Hong Kong
PANalytical OpenLab Mexico
Rigaku OpenLab Colombia
grenoble-darmstadt
Agilent OpenLab Turkey
Bruker OpenLab Indonesia
Bruker OpenLab Uruguay
Rigaku OpenLab Cambodia
PANalytical OpenLab Ghana
Bruker OpenLab Morocco
Agilent OpenLab Argentina
Bruker OpenLab Pakistan

- Chapter 1. Introduction
- Chapter 2. X-rays
- Chapter 3. Crystallography
- Chapter 4. Laue's discovery
- Chapter 5. The immediate sequels to Laue's discovery
- Chapter 6. The principles of X-ray diffraction
- Chapter 7. Methods and problems of crystal structure analysis
- Chapter 8. The growing power of X-ray analysis
- Chapter 9. Problems of inorganic structures
- Chapter 10. Problems of organic structures
- Chapter 11. The growing field of mineral structures
- Chapter 12. Applications of X-ray diffraction to metallurgical science
- Chapter 13. Problems of biochemical structures
- Chapter 14. X-ray diffraction and its impact on physics
- Chapter 15. Dynamical x-ray optics; electron and neutron diffraction
- Chapter 16. X-ray spectroscopy
- Max von Laue
- William Henry Bragg
- Shoji Nishikawa
- Charles Mauguin
- E. S. Fedorov
- Artur Schoenflies
- William Thomas Astbury
- Carl H. Hermann
- Gosta Phragmen
- Victor Moritz Goldschmidt
- Christen Johannes Finbak
- Paul Knipping
- Memorial tablets
- British and Commonwealth schools of crystallography
- The Development of X-ray Diffraction in USA
- The New Crystallography in France
- Germany
- The Netherlands
- Scandinavia
- Japan
- Schools of X-ray Structural Analysis in the Soviet Union
- The World-wide Spread of X-ray Diffraction Methods
- E.N. da C. Andrade
- K. Banerjee
- N. V. Belov
- J. D. Bernal
- J. M. Bijvoet
- W. L. Bragg
- J. C. M. Brentano
- M. J. Buerger
- C. L. Burdick
- C. G. Darwin
- J. D. H. Donnay
- R. Glocker
- A. Guinier
- G. Hagg
- Albert W. Hull
- R. W. James
- H. Lipson
- K. Lonsdale
- H. Mark
- Isamu Nitta
- A. L. Patterson
- Linus Pauling
- Michael Polanyi
- J. Monteath Robertson
- Paul Scherrer
- A. V. Shubnikov
- M. E. Straumanis
- Jean Jacques Trillat
- B. E. Warren
- A. Westgren
- A. J. C. Wilson
- W. A. Wooster
- Jean Wyart
- Ralph W. G. Wyckoff
- The consolidation of the new crystallography
- Biographical notes on authors

Extract from *50 Years of X-ray Diffraction*, edited by P. P. Ewald

It is difficult to set down memories of how an idea was born. After twenty years they become befogged and coloured by the knowledge of later events, and the strict discipline of scientific writing is hard to shake off. Nevertheless, on the occasion of the commemoration of the discovery of X-ray diffraction and at the request of the President of the International Union of Crystallography, the attempt must be made.

In 1942 Yü submitted to *Nature* a paper on the determination of absolute from relative X-ray intensities, and the Editors of *Nature* sent the paper to the Cavendish Laboratory for an opinion on its merit. The method proposed was complex and depended on the use of a set of tables not then available in Britain, but Lipson and I did recommend publication (Yü, 1942). The proposal set us arguing over a practicable method of achieving the same purpose, and a hazy idea emerged that the general level of the intensities of the various reflections from a crystal must depend on the content of the unit cell and not on the details of the atomic arrangement. Lipson (unpublished, so far as I know) suggested calculating the *F*'s for an arbitrary arrangement of the atoms in the unit cell and comparing ∑|*F*_{calc}| with ∑|*F*_{obs}| for suitable groups of reflections, but I wanted a tidier approach. Statistical calculations were in my mind in connection with diffraction by disordered structures like Co and AuCu_{3} (Wilson 1942a, 1943), and it was soon evident that the appropriate statistical variables to use were the X-ray intensities, not the structure amplitudes. A very short calculation (Wilson 1942b) showed that the mean value of the intensity expressed in units of (electrons)^{2} is equal to the sum of the squares of the scattering factors of all the atoms in the unit cell. Once obtained, this relation is practically obvious from conservation of energy, and is the first example of the blindness to the implications of what I knew, that has mingled a good deal of self-dissatisfaction with my pleasure in developing statistical methods.

Knowing the mean value of the intensities immediately suggests the problem of determining the probability distribution of the intensities about the mean. I derived what I thought was the general formula for this by an application of the method of induction, and found that it gave approximate agreement for copper sulphate (Beevers and Lipson, 1934). I drafted a paper on the subject, which I remember discussing with Ewald as we travelled to London together for some function or other. When revising the draft, however, I noticed that my argument made an implicit assumption of non-centrosymmetry in the atomic arrangement, and that a centrosymmetric arrangement would give a different result. This was an important finding, but I did not see its importance. Instead I put the whole matter on one side for four or five years, feeling that distribution functions that depended on symmetry were too complicated to bother with. I ought, of course, to have looked at the matter the other way, and have seen that the distribution function provided a valuable way of detecting those symmetry elements that do not cause systematic absences.

Enlightenment came some years later, when I was in Cardiff and responsible for a research student who found difficulty in distinguishing between a centrosymmetric and a non-centrosymmetric space group having the same systematic absences. There could have been many ways out of his difficulty, but while discussing the problem with Rogers I saw my work on distribution functions from the obverse, and fruitful, point of view (Wilson, 1949). X-ray determination of the absence of a centre of symmetry was received with a little scepticism at first - did not all the textbooks say that it was impossible? - and I well remember carrying a couple of slides in my pocket to a conference of the Institute of Physics, without being able to obtain an opportunity of projecting them. The friends to whom I showed them during the intervals hid their disbelief with varying degrees of success.

Statistical methods of determining the absence of mirror planes and rotation axes provide a third instance of blindness to the obvious. In my letter in *Nature* (1942b) I wrote:

'If two atoms are close together in the projection, they ought to be counted as a single atom with atomic factor equal to the sum of their respective atomic factors. . . . certain coincidences can be predicted from the space group only, and allowed for.'

I was then considering the matter in the direction: space group known; can one avoid statistical complications? It was not until many years later, in conversation with Rogers about ridges of high density in Patterson projections, that the reverse question occurred to me: statistical anomalies detectable; what is the space group? Once the question had been posed it was easy enough for me to write down the factor multiplying the average intensity for the groups of reflections affected by various symmetry elements (Wilson, 1950), and with rather more labour Rogers (1950) was able to prepare the statistical equivalent of vol. I of the *International Tables*.

If there is any moral it is this: systematic work will usually discover the answer to a properly posed question, but discovery of the right questions to ask is a pretty erratic random variable.

1. C. A. Beevers and H. Lipson, 1934. *Proc. Roy. Soc.*, A*146*, 570.

2. D. Rogers, 1950. *Acta Crystallogr.*, *3*, 455.

3. A. J. C. Wilson, 1942a. *Proc. Roy. Soc.*, A*180*, 277.

4. A. J. C. Wilson, 1942b. *Nature*, *150*, 152.

5. A. J. C. Wilson, 1943. *Proc. Roy. Soc.*, A*181*, 360.

6. A. J. C. Wilson, 1949. *Acta Crystallogr.*, *2*, 318.

7. A. J. C. Wilson, 1950. *Acta Crystallogr.*, *3*, 258.

8. S. H. Yü, 1942. *Nature*, *150*, 151.

First published for the International Union of Crystallography 1962 by N.V.A. Oosthoek's Uitgeversmaatschappij, Utrecht, The Netherlands

Digitised 1999 for the IUCr XVIII Congress, Glasgow, Scotland

© 1962, 1999 International Union of Crystallography

The International Union of Crystallography is a non-profit scientific union serving the world-wide interests of crystallographers and other scientists employing crystallographic methods.

© International Union of Crystallography